An Enumeration of the Primitive Recursive Functions without Repetition

In a theorem and its corollary [1] Friedberg gave an enumeration of all the recursively enumerable sets without repetition and an enumeration of all the partial recursive functions without repetition. This note is to prove a similar theorem for the primitive recursive functions. The proof is only a classical one. We shall show that the theorem is intuitionistically unprovable in the sense of Kleene [2]. For similar reason the theorem by Friedberg is also intuitionistically unprovable, which is not stated in his paper.